Asymptotic pattern for a periodic lattice model with age structure and global interaction

Abstract

In this paper, we derive a time-periodic lattice model for a single species in a patchy environment, which has age structure and an infinite number of patches connected locally by diffusion. By appealing to the theory of asymptotic speed of propagation and monotonic periodic semiflows for travelling waves, we establish the existence of periodic travelling wave and spreading speed of the model.

Keywords:

• lattice delay differential system
• periodic travelling wave
• spreading speed

AMS Subject Classifications:

• 37L60
• 45J05
• 35K57
• 92D25

Acknowledgement

The author thanks the referee who contributed, by its remarks and suggestions, to improve the paper.